See complete Problem 172 at:
www.gogeometry.com/problem/p172_trapezoid_quadrilaterals_area_midpoint.htm
Trapezoid, Midpoints, Quadrilaterals, Areas. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Friday, September 5, 2008
Elearn Geometry Problem 172
Subscribe to:
Post Comments (Atom)
by Proposed Problem 170,
ReplyDelete[CED]=[ABCD]/2=[BAGF]
Please detail explanation
Delete- Define H and M the intersections of FG x CE and FG x DE (see problem 171)
ReplyDelete- From problem 170, [CED]=[ABCD]/2
- [ABFG]=[DCFG]=[ABCD]/2
- [ABFG]=S1+[HEM] +S2=[DCFG]=[FCH]+S+[DGM]
- From problem 171 : [HEM] =[FCH]+[DGM]
- Therefore S1+S2=S
With the help of problem 170, [CED]=[ABCD]/2,
ReplyDeletealso, it is easy to see that [ABFG]=[ABCD]/2
So, [CED]=[ABFG], and by eliminating the blue area in between, S=S1+S2